%-------------------------------------------------------------------------------
% Step 1
%-------------------------------------------------------------------------------

@article{Mu05,
  author =  {Mo Mu},
  title =   {{PDE.M}art: A Network-based Problem-solving Environment for {PDE}s},
  journal = {ACM Trans. Math. Software.},
  year =    2005,
  volume =  31,
  number =  4,
  pages =   {508--531}
}

%-------------------------------------------------------------------------------
% Step 6
%-------------------------------------------------------------------------------

@article{Kel74,
  author =  {R. Bruce Kellogg},
  title =   {On the {P}oisson equation with intersecting interfaces},
  journal = {Applicable Analysis},
  year  =   1974,
  volume =  4,
  number =  2,
  pages =   {101--129}
}

%-------------------------------------------------------------------------------
% Step 7
%-------------------------------------------------------------------------------

@article{Li2019,
  doi = {10.1007/s10915-019-01102-1},
  url = {https://doi.org/10.1007/s10915-019-01102-1},
  year = {2019},
  month = dec,
  publisher = {Springer Science and Business Media {LLC}},
  volume = {82},
  number = {1},
  author = {Hao Li and Xiangxiong Zhang},
  title = {Superconvergence of $C^0-Q^k$ Finite Element Method for Elliptic Equations with Approximated Coefficients},
  journal = {Journal of Scientific Computing}
}

%-------------------------------------------------------------------------------
% Step 10
%-------------------------------------------------------------------------------

@incollection{Cangiani2012,
  doi = {10.1007/978-3-642-33134-3_34},
  url = {https://doi.org/10.1007/978-3-642-33134-3_34},
  year = {2012},
  month = nov,
  publisher = {Springer Berlin Heidelberg},
  pages = {315--322},
  author = {A. Cangiani and J. Chapman and E. H. Georgoulis and M. Jensen},
  title = {Implementation of the Continuous-Discontinuous Galerkin Finite Element Method},
  booktitle = {Numerical Mathematics and Advanced Applications 2011}
}

%-------------------------------------------------------------------------------
% Step 14
%-------------------------------------------------------------------------------

@inproceedings{Ban00w,
  author =  {Wolfgang Bangerth},
  title =   {Mesh Adaptivity and Error Control for a Finite Element
             Approximation of the Elastic Wave Equation},
  booktitle =   {Proceedings of the Fifth International Conference on Mathematical
                 and Numerical Aspects of Wave Propagation (Waves2000), Santiago
                 de Compostela, Spain, 2000},
  year =    2000,
  editor =  {Alfredo Berm\'udez and Dolores G\'omez and Christophe Hazard and
             Patrick Joly and Jean E. Roberts},
  publisher =   {SIAM},
  pages =   {725--729}
}

@phdthesis{Ban02,
  author =  {Wolfgang Bangerth},
  title =   {Adaptive Finite Element Methods for the Identification
             of Distributed Parameters in Partial Differential Equations},
  school =  {University of Heidelberg},
  year =    2002
}

@article{BR99b,
  author =  {Wolfgang Bangerth and Rolf Rannacher},
  title =   {Finite element approximation of the acoustic wave equation: {E}rror
             control and mesh adaptation},
  journal = {East--West J. Numer. Math.},
  year =    1999,
  volume =  7,
  number =  4,
  pages =   {263--282}
}

@book{BR03,
  author =  {Wolfgang Bangerth and Rolf Rannacher},
  title =   {Adaptive Finite Element Methods for Differential Equations},
  publisher =   {Birkh{\"a}user Verlag},
  year =    2003
}

@article{BR01a,
  author =  {Wolfgang Bangerth and Rolf Rannacher},
  title =   {Adaptive Finite Element Techniques for the Acoustic Wave Equation},
  journal = {J. Comput. Acoustics},
  year =    2001,
  volume =  9,
  number =  2,
  pages =   {575--591}
}

@article{BR01,
  author =  {Roland Becker and Rolf Rannacher},
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             adaptation in finite element methods.},
  journal = {Acta Numerica},
  year =    2001,
  volume =  10,
  pages =   {1--102}
}

@phdthesis{Bec95,
  author =  {Roland Becker},
  title =   {An Adaptive Finite Element Method for the Incompressible
             {N}avier-{S}tokes Equations on Time-dependent Domains},
  school =  {Universit{\"a}t Heidelberg},
  type =    {Dissertation},
  year =    1995
}

@techreport{Bec98,
  author =  {Roland Becker},
  title =   {Weighted Error Estimators for the Incompressible {N}avier-{S}tokes Equations},
  institution = {Universit{\"a}t Heidelberg},
  type =    {Preprint 98-20},
  year =    1998
}

@article{BR96r,
  author =  {Roland Becker and Rolf Rannacher},
  title =   {A Feed-Back Approach to Error Control in Finite Element Methods:
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  volume =  4,
  year =    1996,
  pages =   {237--264}
}

@inproceedings{BR95,
  author =  {Roland Becker and Rolf Rannacher},
  title =   {Weighted A Posteriori Error Control in {FE} Methods},
  booktitle =   {ENUMATH 97},
  editor =  {H. G. Bock et al.},
  publisher =   {World Scientific Publ., Singapore},
  year =    1998,
  pages =   {621--637}
}

@article{FK97,
  author =  {Christian F{\"u}hrer and Guido Kanschat},
  title =   {A posteriori error control in radiative transfer},
  journal = {Computing},
  year =    1997,
  volume =  58,
  number =  4,
  pages =   {317--334}
}

@phdthesis{Har02,
  author =  {Ralf Hartmann},
  title =   {Adaptive Finite Element Methods for the Compressible {E}uler Equations},
  school =  {Universit{\"a}t Heidelberg},
  year =    2002
}

@article{HH01,
  author =  {Ralf Hartmann and Paul Houston},
  title =   {Adaptive Discontinuous {G}alerkin Finite Element Methods for
             Nonlinear Hyperbolic Conservation Laws},
  publisher =   {SIAM}
  journal = {Journal on Scientific Computing},
  year =    2003,
  volume =  24,
  number =  3,
  pages =   {979--1004}
}

@article{HH01b,
  author =  {Ralf Hartmann and Paul Houston},
  title =   {Adaptive Discontinuous {G}alerkin Finite Element Methods for the
             Compressible {E}uler Equations},
  journal = {Journal of Computational Physics},
  year =    2002,
  volume =  183,
  number =  2,
  pages =   {508--532}
}

@phdthesis{Kan96,
  author =  {Guido Kanschat},
  title =   {Parallel and Adaptive Galerkin Methods for Radiative Transfer Problems},
  school =  {Universit{\"a}t Heidelberg},
  type =    {Dissertation},
  year =    1996
}

@article{RS97,
  author =  {Rolf Rannacher and Franz-Theo Suttmeier},
  title =   {A feed-back approach to error control in finite element methods:
             Application to linear elasticity},
  journal = {Computational Mechanics},
  year =    1997,
  volume =  19,
  number =  5,
  pages =   {434--446}
}

@article{RS98c,
  author =  {Rolf Rannacher and Franz-Theo Suttmeier},
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             techniques: Application to perfect plasticity},
  journal = {Computational Mechanics},
  year =    1998,
  volume =  21,
  number =  2,
  pages =   {123--133}
}

@article{RS99,
  author =  {Rolf Rannacher and Franz-Theo Suttmeier},
  title =   {A posteriori error estimation and mesh adaptation for finite
             element models in elasto-plasticity},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year =    1999,
  volume =  176,
  number =  1,
  pages =   {333--361}
}

@phdthesis{Sut96,
  author =  {Franz-Theo Suttmeier},
  title =   {Adaptive Finite Element Approximation of Problems in
             Elasto-Plasticity Theory},
  school =  {Universit{\"a}t Heidelberg},
  type =    {Dissertation},
  year =    1996
}


%-------------------------------------------------------------------------------
% Step 18
%-------------------------------------------------------------------------------

@article{CTZ04,
  author =  {Stéphane Commend and Andrzej Truty and Thomas Zimmermann},
  title =   {Stabilized finite elements applied to elastoplasticity: I. Mixed displacement–pressure formulation},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year =    2004,
  volume =  193,
  number =  33,
  pages =   {3559--3586}
}

@article{DL05,
  author =  {Huo-Yuan Duan and Qun Lin},
  title =   {Mixed finite elements of least-squares type for elasticity},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year =    2005,
  volume =  194,
  number =  9,
  pages =   {1093--1112}
}


% ------------------------------------
% Step 22
% ------------------------------------

@Article{SW94,
  author = 	 {D. Silvester and A. Wathen},
  title = 	 {Fast iterative solution of stabilised {S}tokes systems. {P}art
                  {II}: {U}sing general block preconditioners},
  journal = 	 {SIAM J. Numer. Anal.},
  year = 	 1994,
  volume = 	 31,
  pages = 	 {1352--1367}}


% ------------------------------------
% Step 47
% ------------------------------------

@article{Brenner2005,
  doi = {10.1007/s10915-004-4135-7},
  url = {https://doi.org/10.1007/s10915-004-4135-7},
  year = {2005},
  month = jun,
  publisher = {Springer Science and Business Media {LLC}},
  volume = {22-23},
  number = {1-3},
  pages = {83--118},
  author = {Susanne C. Brenner and Li-Yeng Sung},
  title = {$C^0$ Interior Penalty Methods for Fourth Order Elliptic Boundary Value Problems on Polygonal Domains},
  journal = {Journal of Scientific Computing}
}


@incollection{Brenner2011,
  doi = {10.1007/978-3-642-23914-4_2},
  url = {https://doi.org/10.1007/978-3-642-23914-4_2},
  year = {2011},
  publisher = {Springer Berlin Heidelberg},
  pages = {79--147},
  author = {Susanne C. Brenner},
  title = {$C^0$ Interior Penalty Methods},
  booktitle = {Lecture Notes in Computational Science and Engineering}
}

@article{Engel2002,
  doi = {10.1016/s0045-7825(02)00286-4},
  url = {https://doi.org/10.1016/s0045-7825(02)00286-4},
  year = {2002},
  month = jul,
  publisher = {Elsevier {BV}},
  volume = {191},
  number = {34},
  pages = {3669--3750},
  author = {G. Engel and K. Garikipati and T.J.R. Hughes and M.G. Larson and L. Mazzei and R.L. Taylor},
  title = {Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates,  and strain gradient elasticity},
  journal = {Computer Methods in Applied Mechanics and Engineering}
}

@article{Brenner2009,
  doi = {10.1093/imanum/drn057},
  url = {https://doi.org/10.1093/imanum/drn057},
  year = {2009},
  month = mar,
  publisher = {Oxford University Press ({OUP})},
  volume = {30},
  number = {3},
  pages = {777--798},
  author = {S. C. Brenner and T. Gudi and L.-y. Sung},
  title = {An a posteriori error estimator for a quadratic C0-interior penalty method for the biharmonic problem},
  journal = {{IMA} Journal of Numerical Analysis}
}

@article{Wells2007,
  doi = {10.1016/j.cma.2007.03.008},
  url = {https://doi.org/10.1016/j.cma.2007.03.008},
  year = {2007},
  month = jul,
  publisher = {Elsevier {BV}},
  volume = {196},
  number = {35-36},
  pages = {3370--3380},
  author = {Garth N. Wells and Nguyen Tien Dung},
  title = {A C0 discontinuous Galerkin formulation for Kirchhoff plates},
  journal = {Computer Methods in Applied Mechanics and Engineering}
}

% ------------------------------------
% Step 50
% ------------------------------------

@article{karakashian2003posteriori,
  title={A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems},
  author={Karakashian, Ohannes A and Pascal, Frederic},
  journal={SIAM Journal on Numerical Analysis},
  volume={41},
  number={6},
  pages={2374--2399},
  year={2003},
  publisher={SIAM}
}

% ------------------------------------
% Step 51
% ------------------------------------

@article {Ngu2012,
    AUTHOR = {Nguyen, N. C. and Peraire, J.},
     TITLE = {Hybridizable discontinuous {G}alerkin methods for partial
              differential equations in continuum mechanics},
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  FJOURNAL = {Journal of Computational Physics},
    VOLUME = {231},
      YEAR = {2012},
    NUMBER = {18},
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      ISSN = {0021-9991},
   MRCLASS = {65N30},
  MRNUMBER = {2954837},
       DOI = {10.1016/j.jcp.2012.02.033},
       URL = {https://doi.org/10.1016/j.jcp.2012.02.033},
}

@incollection{F65,
  author = {Fraeijs de Veubeke, B. X.},
  title = {Displacement and equilibrium models in the finite element method},
  booktitle = {Stress Analysis},
  publisher = {Wiley, New York},
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  year = {1965},
  pages = {275-284},
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}

@article{G65,
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}

@article {CGL2009,
    AUTHOR = {Cockburn, Bernardo and Gopalakrishnan, Jayadeep and Lazarov, Raytcho},
     TITLE = {Unified hybridization of discontinuous {G}alerkin, mixed, and
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              problems},
   JOURNAL = {SIAM J. Numer. Anal.},
  FJOURNAL = {SIAM Journal on Numerical Analysis},
    VOLUME = {47},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {1319--1365},
      ISSN = {0036-1429},
   MRCLASS = {65N30},
  MRNUMBER = {2485455},
MRREVIEWER = {Jose Luis Gracia},
       DOI = {10.1137/070706616},
       URL = {http://dx.doi.org/10.1137/070706616},
}

% ------------------------------------
% Step 55
% ------------------------------------

@Book{elman2005,
  Title                    = {Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics},
  Author                   = {Elman, H. C. and Silvester, D. J. and Wathen, A. J.},
  Publisher                = {Oxford University Press},
  Year                     = {2005},
  Address                  = {Oxford, New York},
  Series                   = {Numerical Mathematics and Scientific Computation},
  ISBN                     = {0-19-852868-X},
}

@inproceedings{kovasznay1948laminar,
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  number={1},
  pages={58--62},
  year={1948},
  organization={Cambridge University Press}
}


% ------------------------------------
% Step 61
% ------------------------------------

@incollection{Wang2019,
  doi = {10.1007/978-3-030-22747-0_37},
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  pages = {495--509},
  author = {Zhuoran Wang and Graham Harper and Patrick O'Leary and Jiangguo Liu and Simon Tavener},
  title = {deal.{II} Implementation of a Weak Galerkin Finite Element Solver for Darcy Flow},
  booktitle = {Lecture Notes in Computer Science}
}

% ------------------------------------
% Step 63
% ------------------------------------

@incollection{john2006discontinuity,
  title={On discontinuity—capturing methods for convection—diffusion equations},
  author={John, Volker and Knobloch, Petr},
  booktitle={Numerical Mathematics and Advanced Applications},
  pages={336--344},
  year={2006},
  publisher={Springer}
}

@article{KanschatNotesIterative,
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  year={2015},
  url={https://www.mathsim.eu/~gkanscha/notes/C.pdf}
}

@book{smith2004domain,
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  publisher={Cambridge University Press}
}

@book{toselli2006domain,
  title={Domain decomposition methods-algorithms and theory},
  author={Toselli, Andrea and Widlund, Olof},
  volume={34},
  year={2006},
  publisher={Springer Science \& Business Media}
}

% ------------------------------------
% Step 67
% ------------------------------------

@article{KennedyCarpenterLewis2000,
author = {Kennedy, Christopher A. and Carpenter, Mark H. and Lewis, R. Micheal},
title = {Low-storage, explicit {R}unge--{K}utta schemes for the compressible {N}avier--{S}tokes equations},
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volume = 35,
year = 2000,
pages = {177--219},
doi = {10.1016/S0168-9274(99)00141-5},
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}

@article{TseliosSimos2007,
author = {Tselios, Kostas and Simos, Theodore E.},
title = {Optimized {R}unge--{K}utta methods with minimal dispersion and dissipation for problems arising from computational acoustics},
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volume = 363,
year = 2007,
pages = {38--48},
doi = {10.1016/j.physleta.2006.10.072},
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}

@article{KronbichlerSchoeder2016,
author = {Kronbichler, Martin and Schoeder, Svenja and M\"uller, Christopher and Wall, Wolfgang A.},
title = {Comparison of implicit and explicit hybridizable discontinuous {G}alerkin methods for the acoustic wave equation},
journal = {International Journal for Numerical Methods in Engineering},
volume = "106",
number = 9,
pages = "712--739",
doi = {10.1002/nme.5137},
url = {https://doi.org/10.1002/nme.5137},
year = {2016}
}

@article{SchoederKormann2018,
  title={Efficient explicit time stepping of high order discontinuous {G}alerkin schemes for waves},
  author={Schoeder, Svenja and Kormann, Katharina and Wall, Wolfgang A. and  Kronbichler, Martin},
  journal={SIAM J. Sci. Comput.},
  pages = {C803--C826},
  volume = 40,
  number = 6,
  year={2018},
  doi={10.1137/18M1185399},
  url={https://doi.org/10.1137/18M1185399}
}


@article{FehnWallKronbichler2019,
author = {Fehn, Niklas and Wall, Wolfgang A. and Kronbichler, Martin},
title = {A matrix-free high-order discontinuous {G}alerkin compressible {N}avier--{S}tokes solver:
A performance comparison of compressible and incompressible formulations for turbulent incompressible flows},
journal = {International Journal for Numerical Methods in Fluids},
volume = {89},
number = {3},
pages = {71--102},
year = {2019},
doi = {10.1002/fld.4683},
url = {https://doi.org/10.1002/fld.4683}
}

@article{KronbichlerKormann2019,
author = {Kronbichler, Martin and Kormann, Katharina},
title  = {Fast matrix-free evaluation of discontinuous {G}alerkin finite element operators},
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number = {3},
pages = {29:1--29:40},
year = {2019},
doi = {10.1145/3325864},
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}

@article{Gassner2013,
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  pages = {A1233--A1253},
  author = {Gregor J. Gassner},
  title = {A Skew-Symmetric Discontinuous {G}alerkin Spectral Element Discretization and Its Relation to {SBP}-{SAT} Finite Difference Methods},
  journal = {{SIAM} Journal on Scientific Computing}
}

% ------------------------------------
% Step 68
% ------------------------------------

@article{Blais2013,
  title={Dealing with more than two materials in the FVCF--ENIP method},
  author={Blais, Bruno and Braeunig, Jean-Philippe and Chauveheid, Daniel and Ghidaglia, Jean-Michel and Loub{\`e}re, Rapha{\"e}l},
  journal={European Journal of Mechanics-B/Fluids},
  volume={42},
  pages={1--9},
  year={2013},
  publisher={Elsevier}
}

@article{Blais2019,
  title={Experimental Methods in Chemical Engineering: Discrete Element Method—DEM},
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  volume={97},
  number={7},
  pages={1964--1973},
  year={2019},
  publisher={Wiley Online Library}
}

@article{Gassmoller2019,
  title={Evaluating the accuracy of hybrid finite element/particle-in-cell methods for modelling incompressible Stokes flow},
  author={Gassm{\"o}ller, Rene and Lokavarapu, Harsha and Bangerth, Wolfgang and Puckett, Elbridge Gerry},
  journal={Geophysical Journal International},
  volume={219},
  number={3},
  pages={1915--1938},
  year={2019},
  publisher={Oxford University Press}
}


% ------------------------------------
% Step 69
% ------------------------------------

@article {GuermondPopov2016,
    AUTHOR = {Guermond, Jean-Luc and Popov, Bojan},
     TITLE = {Invariant domains and first-order continuous finite element
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   JOURNAL = {SIAM J. Numer. Anal.},
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      YEAR = {2016},
    NUMBER = {4},
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      ISSN = {0036-1429},
       DOI = {10.1137/16M1074291},
}

@article {GuermondPopov2016b,
    AUTHOR = {Guermond, Jean-Luc and Popov, Bojan},
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@article {GuermondEtAl2018,
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@book {GuermondErn2004,
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@article {Brooks1982,
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      NOTE = {FENOMECH ''81, Part I (Stuttgart, 1981)},
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@article {Johnson1986,
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@book{Rainald2008,
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% ------------------------------------
% Step 70
% ------------------------------------



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% ------------------------------------
% References used elsewhere
% ------------------------------------

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